This is an interesting analysis as we see that for 3 Tails 2 Heads / 3 Heads 2 Tails and More Tails Than Heads / More Heads Than Tails wagers at the 2 σ range, the expectation already goes against the house, being a positive expectation for the player.

1 σ

Breakeven Odds at 1 σ

2 σ

Breakeven Odds at 2 σ

3 σ

Breakeven Odds at 3 σ

5 Tails / Heads

Mean + (SD x 1)

= 0.205243

(1-0.205243)/ 0.205243

= 3.872282

Mean + (SD x 2)

= 0.379235

(1-0.379235)/ 0.379235

= 1.636886

Mean + (SD x 3)

= 0.553228

(1-0.553228)/ 0.553228

= 0.807573

4 Tails 1 Head / 4 Heads 1 Tail

Mean + (SD x 1)

= 0.519342

(1-0.519342)/ 0.519342

= 0.925513

Mean + (SD x 2)

= 0.882434

(1-0.882434)/ 0.882434

= 0.133229

Mean + (SD x 3)

= 1.245527

(1-1.245527)/ 1.245527

= -0.19713

3 Tails 2 Heads / 3 Heads 2 Tails

Mean + (SD x 1)

= 0.776012

(1-0.776012)/ 0.776012

= 0.288639

Mean + (SD x 2)

= 1.239525

(1-1.239525)/ 1.239525

= -0.19324

Mean + (SD x 3)

= 1.703037

(1-1.703037)/ 1.703037

= -0.41281

More Tails Than Heads / More Heads Than Tails

Mean + (SD x 1)

= 0.967772

(1-0.967772)/ 0.967772

= 0.033301

Mean + (SD x 2)

= 1.466795

(1-1.466795)/ 1.466795

= -0.31824

Mean + (SD x 3)

= 1.965817

(1-1.965817)/ 1.965817

= -0.49131

Not to worry, as the 2 σ is expected to occur only 15% of the time and as σ swings bothways, going into the positive as well as negative, everyone else (85%) will lose either at the probability range or more.

This should also tell you that you would expect a higher level of variation in your results with the 3 Tails 2 Heads / 3 Heads 2 Tails and More Tails Than Heads / More Heads Than Tails wagers, with the house winning almost all the time for the other wager types.